Finite Group Databasebeta

← #13169237

Subgroups — #13169237

Order 1728.

1372 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723676C211yesmaximal, characteristic, complemented
2#11723542C211yesmaximal, characteristic, complemented
3#11723525C211yesmaximal, characteristic, complemented
4#11723494C211yesmaximal, characteristic, complemented
5C3×#63915C211yesmaximal, characteristic, complemented
6C3×#63890C211yesmaximal, characteristic, complemented
7C3×#63858C211yesmaximal, characteristic, complemented
8#11723003C211yesmaximal, characteristic, complemented
9#11722996C211yesmaximal, characteristic, complemented
10#11722973C211yesmaximal, characteristic, complemented
11#11722963C211yesmaximal, characteristic, complemented
12#11722958C211yesmaximal, characteristic, complemented
13#11722949C211yesmaximal, characteristic, complemented
14#11722932C211yesmaximal, characteristic, complemented
15#11722906C211yesmaximal, characteristic, complemented
16#10594657—31nomaximal
17#10594307—31nomaximal
18#10594162—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
21C2×#6292C2211yescharacteristic
22C2×#6291C2211yescharacteristic
23C2×#6291C2211yescharacteristic
24C2×#6291C2211yescharacteristic, complemented
25C2×#6289C2211yescharacteristic
26C2×#6289C2211yescharacteristic
27C2×#6289C2211yescharacteristic, complemented
28C2×C3×#627C2211yescharacteristic, complemented
29C2×C3×#626C2211yescharacteristic
30C2×C3×#625C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic, complemented
32C3×#3752C2211yescharacteristic
33C3×#3750C2211yescharacteristic, complemented
34C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C32×C4⋊Dic3C2211yescharacteristic, complemented
38#88815C2211yescharacteristic, complemented
39#88815C2211yescharacteristic, complemented
40#88814C2211yescharacteristic
41#88814C2211yescharacteristic
42#88804C2211yescharacteristic
43#88804C2211yescharacteristic
44#88804C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64102—31no—
55#64093—31no—
56#64091—31no—
57C3×#898—31no—
58C3×#894—31no—
59C3×#886—31no—
60C3×#885—31no—
61C3×#885—31no—
62C3×#879—31no—
63#63983—31no—
64#63981—31no—
65#63978—31no—
66#63975—31no—
67#63974—31no—
68#63971—31no—
69#63958—31no—
70#63952—31no—
71#63923—31no—
72#63923—31no—
73#63923—61no—
74#63922—31no—
75#63921—31no—
76#63921—31no—
77#63916—31no—
78#63915D311yescharacteristic, complemented
79#63910—31no—
80#63910—31no—
81#63910—31no—
82#63910—61no—
83#63907—31no—
84#63906—31no—
85C4×#626—31no—
86#63895—31no—
87#63894—31no—
88#63894—31no—
89#63894—61no—
90#63890D311yescharacteristic, complemented
91#63888—31no—
92#63880—31no—
93#63871—31no—
94#63868—31no—
95#63864—31no—
96#63862—31no—
97#63859—31no—
98#63858D311yescharacteristic, complemented
99#63854—31no—
100#63853—31no—
101#63852—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×D3×C3⋊D3—22no—
108C2×D3×C3⋊D3—41no—
109C2×D3×C3⋊D3—41no—
110C2×C33×C4C2311yescharacteristic
111C4⋊(C3⋊(C3⋊D3))—22no—
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6292—41no—
122#6291—22no—
123#6291—41no—
124#6291—41no—
125#6289—41no—
126#6289—41no—
127#6289—41no—
128C3×#627—41no—
129C3×#626—41no—
130C3×#625—41no—
131C3×D3×Dic3—41no—
132#5704—91no—
133#5678—91no—
134#5657—91no—
135C23×C3⋊D3—31no—
136C22×D32—31no—
137C22×D32—31no—
138C22×D32—61no—
139C2×#638—31no—
140C2×#638—31no—
141C2×#638—31no—
142C2×C4⋊(C3⋊D3)—31no—
143C2×C4⋊(C3⋊D3)—31no—
144C2×C4⋊(C3⋊D3)—31no—
145C2×C4⋊(C3⋊D3)—31no—
146C2×C4⋊(C3⋊D3)—61no—
147C2×C4⋊(C3⋊D3)—61no—
148C2×C4⋊(C3⋊D3)—61no—
149C2×C4⋊(C3⋊D3)—121no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—31no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C22×C3×Dic3—31no—
157C2×C3×D12—31no—
158C2×C3×C4×D3—31no—
159C2×C3×Dic6—31no—
160C2×C3×Dic6—31no—
161C2×#627C2×D311yescharacteristic, complemented
162C2×#626—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#626—31no—
166C2×#626—31no—
167C2×#626—31no—
168C2×#626—31no—
169C2×#626—31no—
170C2×#626—61no—
171C2×#626—61no—
172C2×#626—61no—
173C2×#626—61no—
174C2×#626C2×D311yescharacteristic
175C2×#625C2×D311yescharacteristic
176C2×#624—31no—
177C2×#624—31no—
178C2×#624—31no—
179C2×#624—31no—
180C2×#624—31no—
181C2×#624—31no—
182C2×#624—61no—
183C2×#624—61no—
184C2×#624—61no—
185C2×D3×Dic3C2×D311yescharacteristic, complemented
186C32×C4⋊C4—31no—
187C32×C22⋊C4—31no—
188C32×C22⋊C4—31no—
189#3752—31no—
190#3752—31no—
191#3752—31no—
192#3752—31no—
193#3752C2×D311yescharacteristic
194#3750C2×D311yescharacteristic, complemented
195C4×C3⋊Dic3C2×D311yescharacteristic, complemented
196C3×#217—31no—
197C3×#217—31no—
198C3×#217—31no—
199C3×#217—31no—
200C3×(C2×D3)⋊C4—21no—
201C3×(C2×D3)⋊C4—21no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—61no—
211C3×(C2×D3)⋊C4C2×D311yescharacteristic
212C3×(C2×D3)⋊C4C2×D311yescharacteristic
213C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
214C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
215C3×C4⋊Dic3—21no—
216C3×C4⋊Dic3—31no—
217C3×C4⋊Dic3—31no—
218C3×C4⋊Dic3C2×D311yescharacteristic, complemented
219C3×C4⋊Dic3C2×D311yescharacteristic, complemented
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—61no—
225C3×C4×Dic3—31no—
226C3×C4×Dic3—31no—
227C3×C4×Dic3—31no—
228C3×C4×Dic3—31no—
229C3×C4×Dic3—61no—
230#3724—31no—
231#3724—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3C2×D311yescharacteristic, complemented
237Dic3⋊Dic3C2×D311yescharacteristic, complemented
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244#3722—31no—
245#3722—31no—
246#3722—31no—
247#3722—31no—
248#3722—61no—
249#3722—61no—
250#3722—61no—
251#3722—61no—
252#3722C2×D311yescharacteristic
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—31no—
257(C2×D3)⋊Dic3C2×D311yescharacteristic
258(C2×D3)⋊Dic3C2×D311yescharacteristic
259(C2×D3)⋊Dic3C2×D311yescharacteristic
260(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
261Dic32C2×D311yescharacteristic, complemented
262C22×C33C2411yescharacteristic
263C2×C3⋊(C3⋊D3)—21no—
264C2×C3⋊(C3⋊D3)—21no—
265C2×C3⋊(C3⋊D3)—21no—
266C2×C3⋊(C3⋊D3)—21no—
267C2×C3⋊(C3⋊D3)—21no—
268C2×C3⋊(C3⋊D3)#4112yes—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C2×C32×D3—21no—
273C2×C32×D3—21no—
274C2×C32×D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278D3×C3⋊D3—44no—
279C33×C4—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C3×C3⋊Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#126—91no—
290C3×#124—91no—
291C3×#123—91no—
292#947—91no—
293#946—91no—
294#939—91no—
295#938—91no—
296#937—91no—
297#937—91no—
298#930—91no—
299C4×#67—91no—
300#898—31no—
301#898—91no—
302#897—91no—
303#896—91no—
304#895—91no—
305#895—91no—
306#894—31no—
307#894—91no—
308#893—91no—
309#893—91no—
310#893—181no—
311#886—31no—
312#885—31no—
313#885—31no—
314#885—91no—
315#884—91no—
316#884—91no—
317#884—91no—
318#884—91no—
319#884—181no—
320#883—91no—
321#883—91no—
322#882—91no—
323#882—91no—
324#882—91no—
325#882—91no—
326#882—181no—
327#67⋊C4—91no—
328D3×C22⋊C4—91no—
329D3×C22⋊C4—91no—
330D3×C22⋊C4—91no—
331#879—31no—
332#879—91no—
333#876—91no—
334#875—91no—
335C4×D12—91no—
336C4×D12—91no—
337C23×C32—31no—
338C23×C32—31no—
339C22×C3⋊D3—31no—
340C22×C3⋊D3—31no—
341C22×C3⋊D3—31no—
342C22×C3⋊D3—31no—
343C22×C3⋊D3—31no—
344C22×C3⋊D3—31no—
345C22×C3⋊D3—61no—
346C22×C3⋊D3—61no—
347C22×C3⋊D3—61no—
348C22×C3⋊D3—61no—
349C22×C3⋊D3—61no—
350C22×C3⋊D3—61no—
351C22×C3⋊D3—62no—
352C22×C3⋊D3—121no—
353C22×C3⋊D3—121no—
354C22×C3⋊D3—121no—
355C22×C3⋊D3—121no—
356C22×C3⋊D3C22×D311yescharacteristic
357C22×C3×D3—21no—
358C22×C3×D3—21no—
359C22×C3×D3—31no—
360C22×C3×D3—31no—
361C22×C3×D3—61no—
362C22×C3×D3C22×D311yescharacteristic
363C22×C3×D3C22×D311yescharacteristic
364C22×C3×D3C22×D311yescharacteristic
365C22×C3×D3C22×D311yescharacteristic
366C2×D32—62no—
367C2×D32—62no—
368C2×D32—122no—
369C2×D32—121no—
370C2×D32—121no—
371C2×D32—121no—
372C2×D32—121no—
373C2×D32—122no—
374C2×D32—122no—
375C2×C32×C4—21no—
376C2×C32×C4—21no—
377C2×C32×C4—21no—
378C2×C32×C4—31no—
379C2×C32×C4—31no—
380C2×C32×C4—31no—
381C2×C32×C4—31no—
382C2×C32×C4—41no—
383C2×C32×C4C22×D311yescharacteristic
384C2×C32×C4C22×D311yescharacteristic
385C2×C32×C4C22×D311yescharacteristic
386#638—62no—
387#638—121no—
388#638—121no—
389C2×C3⋊Dic3C22×D311yescharacteristic
390C2×C3⋊Dic3C22×D311yescharacteristic
391C2×C3⋊Dic3C22×D311yescharacteristic
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C4⋊(C3⋊D3)—62no—
395C4⋊(C3⋊D3)—62no—
396C4⋊(C3⋊D3)—62no—
397C4⋊(C3⋊D3)—64no—
398C4⋊(C3⋊D3)—122no—
399C4⋊(C3⋊D3)—122no—
400C4⋊(C3⋊D3)—124no—
401C4⋊(C3⋊D3)—121no—
402C4×C3⋊D3—121no—
403C4×C3⋊D3—121no—
404C4×C3⋊D3—121no—
405C3×#67—121no—
406C3×#67—121no—
407C3×#67—121no—
408C2×C3×Dic3—21no—
409C2×C3×Dic3—21no—
410C2×C3×Dic3—21no—
411C2×C3×Dic3—21no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—61no—
424C2×C3×Dic3—61no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3—121no—
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C3×D12—121no—
437C3×C4×D3—121no—
438C3×Dic6—121no—
439C3×Dic6—121no—
440#627—41no—
441#626—41no—
442#626—62no—
443#626—62no—
444#626—122no—
445#626—121no—
446#626—121no—
447#626—122no—
448#626—121no—
449#626—121no—
450#626—121no—
451#626—121no—
452#626—122no—
453#626—122no—
454#625—41no—
455#624—121no—
456#624—121no—
457#624—121no—
458#624—121no—
459#624—121no—
460#624—121no—
461#624—122no—
462#624—122no—
463#624—122no—
464D3×Dic3—41no—
465#538—271noSylow
466C2×C33C2×#4111yescharacteristic
467C2×C33H(5,𝔽2)11yescharacteristic
468C2×C33H(5,𝔽2)11yescharacteristic
469C3⋊(C3⋊D3)—22no—
470C3⋊(C3⋊D3)—41no—
471C3×C3⋊D3—41no—
472C32×D3—41no—
473C32×D3—41no—
474C23×D3—91no—
475C23×D3—91no—
476C23×D3—91no—
477C23×D3—181no—
478C2×C3×Q8—91no—
479C2×C3×D4—91no—
480C2×C3×D4—91no—
481C22×C3×C4—91no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67—31no—
485C2×#67—91no—
486C2×#67—91no—
487C2×#67—91no—
488C2×#67—91no—
489C2×#67—91no—
490C2×#67—91no—
491C2×#67—91no—
492C2×#67—181no—
493C2×#67—181no—
494C2×#67—181no—
495C22×Dic3—31no—
496C2×D12—31no—
497C2×D12—91no—
498C2×D12—91no—
499C2×D12—91no—
500C2×D12—91no—
501C2×D12—91no—
502C2×D12—91no—
503C2×D12—91no—
504C2×D12—91no—
505C2×D12—181no—
506C2×D12—181no—
507C2×D12—181no—
508C2×D12—181no—
509C2×D12—361no—
510C2×C4×D3—31no—
511C2×C4×D3—91no—
512C2×C4×D3—91no—
513C2×C4×D3—91no—
514C2×C4×D3—91no—
515C2×C4×D3—91no—
516C2×C4×D3—91no—
517C2×C4×D3—91no—
518C2×C4×D3—91no—
519C2×C4×D3—91no—
520C2×C4×D3—181no—
521C2×C4×D3—181no—
522C2×C4×D3—181no—
523C2×Dic6—31no—
524C2×Dic6—31no—
525C3×C4⋊C4—31no—
526C3×C4⋊C4—31no—
527C3×C4⋊C4—61no—
528C3×C4⋊C4—91no—
529C3×C4⋊C4—91no—
530C3×C4⋊C4—91no—
531C3×C22⋊C4—31no—
532C3×C22⋊C4—31no—
533C3×C22⋊C4—31no—
534C3×C22⋊C4—31no—
535C3×C22⋊C4—61no—
536C3×C22⋊C4—61no—
537C3×C22⋊C4—91no—
538C3×C22⋊C4—91no—
539C3×C22⋊C4—91no—
540C3×C22⋊C4—91no—
541C3×C22⋊C4—91no—
542C3×C22⋊C4—91no—
543C3×C42—91no—
544C3×C42—91no—
545#217—31no—
546#217—31no—
547#217—31no—
548#217—31no—
549#217—91no—
550#217—91no—
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—31no—
553(C2×D3)⋊C4—31no—
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—31no—
556(C2×D3)⋊C4—31no—
557(C2×D3)⋊C4—31no—
558(C2×D3)⋊C4—31no—
559(C2×D3)⋊C4—61no—
560(C2×D3)⋊C4—91no—
561(C2×D3)⋊C4—91no—
562(C2×D3)⋊C4—91no—
563(C2×D3)⋊C4—91no—
564(C2×D3)⋊C4—91no—
565(C2×D3)⋊C4—91no—
566(C2×D3)⋊C4—91no—
567(C2×D3)⋊C4—91no—
568(C2×D3)⋊C4—91no—
569(C2×D3)⋊C4—91no—
570(C2×D3)⋊C4—91no—
571(C2×D3)⋊C4—91no—
572(C2×D3)⋊C4—91no—
573(C2×D3)⋊C4—91no—
574(C2×D3)⋊C4—91no—
575(C2×D3)⋊C4—91no—
576(C2×D3)⋊C4—181no—
577(C2×D3)⋊C4—181no—
578(C2×D3)⋊C4—181no—
579(C2×D3)⋊C4—181no—
580(C2×D3)⋊C4D3211yescharacteristic
581(C2×D3)⋊C4D3211yescharacteristic, complemented
582C4⋊Dic3—31no—
583C4⋊Dic3—31no—
584C4⋊Dic3—91no—
585C4⋊Dic3—91no—
586C4⋊Dic3D3211yescharacteristic, complemented
587Dic3⋊C4—31no—
588Dic3⋊C4—31no—
589Dic3⋊C4—31no—
590Dic3⋊C4—31no—
591Dic3⋊C4—61no—
592Dic3⋊C4—91no—
593Dic3⋊C4—91no—
594Dic3⋊C4—91no—
595Dic3⋊C4—91no—
596C4×Dic3—31no—
597C4×Dic3—31no—
598C4×Dic3—31no—
599C4×Dic3—31no—
600C4×Dic3—61no—
601C22×C32—21no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—41no—
605C22×C32—61no—
606C22×C32—61no—
607C22×C32—61no—
608C22×C32—61no—
609C22×C32—61no—
610C22×C32—61no—
611C22×C32C23×D311yescharacteristic
612C22×C32C23×D311yescharacteristic
613C22×C32C23×D311yescharacteristic
614C2×C3⋊D3—21no—
615C2×C3⋊D3—21no—
616C2×C3⋊D3—21no—
617C2×C3⋊D3—32no—
618C2×C3⋊D3—32no—
619C2×C3⋊D3—32no—
620C2×C3⋊D3—62no—
621C2×C3⋊D3—62no—
622C2×C3⋊D3—62no—
623C2×C3⋊D3—61no—
624C2×C3⋊D3—61no—
625C2×C3⋊D3—61no—
626C2×C3⋊D3—61no—
627C2×C3⋊D3—61no—
628C2×C3⋊D3—61no—
629C2×C3⋊D3—61no—
630C2×C3⋊D3—62no—
631C2×C3⋊D3—61no—
632C2×C3⋊D3—61no—
633C2×C3⋊D3—61no—
634C2×C3⋊D3—61no—
635C2×C3⋊D3—61no—
636C2×C3⋊D3—61no—
637C2×C3⋊D3—61no—
638C2×C3⋊D3—61no—
639C2×C3⋊D3—122no—
640C2×C3⋊D3—121no—
641C2×C3⋊D3—121no—
642C2×C3⋊D3—122no—
643C2×C3⋊D3—121no—
644C2×C3⋊D3—121no—
645C2×C3⋊D3—121no—
646C2×C3⋊D3—121no—
647C2×C3⋊D3—121no—
648C2×C3⋊D3—121no—
649C2×C3⋊D3—121no—
650C2×C3⋊D3—121no—
651C2×C3⋊D3—121no—
652C2×C3⋊D3—121no—
653C2×C3⋊D3—121no—
654C2×C3⋊D3—121no—
655C2×C3⋊D3—124no—
656C2×C3⋊D3—241no—
657C2×C3⋊D3—241no—
658C2×C3⋊D3—241no—
659C2×C3⋊D3—241no—
660C2×C3×D3—22no—
661C2×C3×D3—21no—
662C2×C3×D3—21no—
663C2×C3×D3—21no—
664C2×C3×D3—21no—
665C2×C3×D3—21no—
666C2×C3×D3—21no—
667C2×C3×D3—21no—
668C2×C3×D3—21no—
669C2×C3×D3—21no—
670C2×C3×D3—21no—
671C2×C3×D3—21no—
672C2×C3×D3—21no—
673C2×C3×D3—41no—
674C2×C3×D3—41no—
675C2×C3×D3—41no—
676C2×C3×D3—41no—
677C2×C3×D3—41no—
678C2×C3×D3—62no—
679C2×C3×D3—61no—
680C2×C3×D3—61no—
681C2×C3×D3—61no—
682C2×C3×D3—61no—
683C2×C3×D3—61no—
684C2×C3×D3—61no—
685C2×C3×D3—121no—
686C2×C3×D3—121no—
687D32—124no—
688D32—124no—
689D32—128no—
690C32×C4—21no—
691C32×C4—22no—
692C32×C4—21no—
693C32×C4—21no—
694C32×C4—41no—
695C32×C4—41no—
696C32×C4—42no—
697C32×C4—61no—
698C32×C4—61no—
699C32×C4—61no—
700C32×C4—61no—
701C3⋊Dic3—21no—
702C3⋊Dic3—21no—
703C3⋊Dic3—21no—
704C3⋊Dic3—21no—
705C3⋊Dic3—21no—
706C3×Dic3—21no—
707C3×Dic3—21no—
708C3×Dic3—21no—
709C3×Dic3—21no—
710C3×Dic3—21no—
711C3×Dic3—21no—
712C3×Dic3—21no—
713C3×Dic3—21no—
714C3×Dic3—41no—
715C3×Dic3—41no—
716C3×Dic3—41no—
717C3×Dic3—41no—
718C3×Dic3—62no—
719C3×Dic3—62no—
720C3×Dic3—61no—
721C3×Dic3—61no—
722C3×Dic3—61no—
723C3×Dic3—61no—
724C3×Dic3—61no—
725C3×Dic3—61no—
726C3×Dic3—61no—
727C3×Dic3—61no—
728C3×Dic3—61no—
729C3×Dic3—61no—
730C3×Dic3—121no—
731C3×Dic3—121no—
732C3×Dic3—121no—
733#126—91no—
734#126—271no—
735#124—91no—
736#124—271no—
737#123—91no—
738#123—271no—
739C22⋊Q8—271no—
740#121—271no—
741#121—271no—
742#121—271no—
743#120—271no—
744#120—271no—
745C4×D4—271no—
746C4×D4—271no—
747C2×C22⋊C4—271no—
748C33#53811yescharacteristic, complemented, Sylow
749C23×C3—31no—
750C23×C3—31no—
751C23×C3—31no—
752C23×C3—31no—
753C23×C3—61no—
754C23×C3—61no—
755C23×C3—91no—
756C22×D3—31no—
757C22×D3—31no—
758C22×D3—61no—
759C22×D3—91no—
760C22×D3—91no—
761C22×D3—91no—
762C22×D3—91no—
763C22×D3—91no—
764C22×D3—91no—
765C22×D3—181no—
766C22×D3—181no—
767C22×D3—181no—
768C22×D3—181no—
769C22×D3—181no—
770C22×D3—181no—
771C22×D3—182no—
772C22×D3—182no—
773C22×D3—182no—
774C22×D3—361no—
775C22×D3—361no—
776C22×D3—362no—
777C22×D3—361no—
778C22×D3—361no—
779C22×D3—361no—
780C22×D3—361no—
781C22×D3—361no—
782C22×D3—361no—
783C22×D3—362no—
784C22×D3—362no—
785C22×D3C2×D3211yescharacteristic
786C22×D3C2×D3211yescharacteristic
787C3×Q8—361no—
788C3×D4—361no—
789C3×D4—361no—
790C2×C3×C4—21no—
791C2×C3×C4—21no—
792C2×C3×C4—21no—
793C2×C3×C4—31no—
794C2×C3×C4—31no—
795C2×C3×C4—31no—
796C2×C3×C4—31no—
797C2×C3×C4—31no—
798C2×C3×C4—31no—
799C2×C3×C4—31no—
800C2×C3×C4—31no—
801C2×C3×C4—41no—
802C2×C3×C4—61no—
803C2×C3×C4—61no—
804C2×C3×C4—61no—
805C2×C3×C4—61no—
806C2×C3×C4—91no—
807C2×C3×C4—91no—
808C2×C3×C4—91no—
809C2×C3×C4—91no—
810C2×C3×C4—91no—
811C2×C3×C4—361no—
812C2×C3×C4C2×D3211yescharacteristic
813C2×C3×C4C2×D3211yescharacteristic
814C2×C3×C4C2×D3211yescharacteristic
815#67—121no—
816#67—121no—
817#67—121no—
818#67—182no—
819#67—182no—
820#67—362no—
821#67—361no—
822#67—361no—
823#67—361no—
824#67—361no—
825#67—361no—
826#67—362no—
827#67—362no—
828C2×Dic3—31no—
829C2×Dic3—31no—
830C2×Dic3—31no—
831C2×Dic3—31no—
832C2×Dic3—31no—
833C2×Dic3—31no—
834C2×Dic3—31no—
835C2×Dic3—31no—
836C2×Dic3—31no—
837C2×Dic3—31no—
838C2×Dic3—61no—
839C2×Dic3—61no—
840C2×Dic3—61no—
841C2×Dic3—61no—
842C2×Dic3—61no—
843C2×Dic3—121no—
844C2×Dic3C2×D3211yescharacteristic
845C2×Dic3C2×D3211yescharacteristic
846C2×Dic3C2×D3211yescharacteristic
847C2×Dic3C2×D3211yescharacteristic
848D12—121no—
849D12—182no—
850D12—182no—
851D12—182no—
852D12—184no—
853D12—182no—
854D12—362no—
855D12—362no—
856D12—364no—
857D12—361no—
858D12—361no—
859D12—362no—
860D12—361no—
861D12—361no—
862C4×D3—121no—
863C4×D3—361no—
864C4×D3—361no—
865C4×D3—361no—
866C4×D3—361no—
867C4×D3—361no—
868C4×D3—361no—
869C4×D3—361no—
870C4×D3—361no—
871C4×D3—361no—
872C4×D3—362no—
873C4×D3—362no—
874C4×D3—362no—
875Dic6—121no—
876Dic6—121no—
877C2×C32—21no—
878C2×C32—21no—
879C2×C32—21no—
880C2×C32—21no—
881C2×C32—21no—
882C2×C32—21no—
883C2×C32—21no—
884C2×C32—21no—
885C2×C32—21no—
886C2×C32—41no—
887C2×C32—41no—
888C2×C32—41no—
889C2×C32—121no—
890C2×C32—121no—
891C2×C32#100411yescharacteristic
892C2×C32#100411yescharacteristic
893C2×C32D3×#4111yescharacteristic
894C2×C32D3×#4111yescharacteristic
895C2×C32D3×#4111yescharacteristic
896C2×C32#100911yescharacteristic
897C2×C32#100911yescharacteristic
898C2×C32#100911yescharacteristic
899C2×C32#100911yescharacteristic
900C3⋊D3—41no—
901C3⋊D3—62no—
902C3⋊D3—62no—
903C3⋊D3—62no—
904C3⋊D3—122no—
905C3⋊D3—122no—
906C3⋊D3—122no—
907C3⋊D3—121no—
908C3⋊D3—122no—
909C3⋊D3—121no—
910C3⋊D3—121no—
911C3⋊D3—242no—
912C3⋊D3—241no—
913C3⋊D3—241no—
914C3⋊D3—242no—
915C3×D3—42no—
916C3×D3—41no—
917C3×D3—41no—
918C3×D3—41no—
919C3×D3—41no—
920C3×D3—81no—
921C3×D3—122no—
922C3×D3—121no—
923C3×D3—121no—
924C24—271no—
925C2×Q8—91no—
926C2×D4—91no—
927C2×D4—91no—
928C2×D4—271no—
929C2×D4—271no—
930C2×D4—271no—
931C2×D4—271no—
932C2×D4—271no—
933C22×C4—91no—
934C22×C4—271no—
935C22×C4—271no—
936C22×C4—271no—
937C4⋊C4—31no—
938C4⋊C4—91no—
939C4⋊C4—91no—
940C4⋊C4—91no—
941C4⋊C4—271no—
942C4⋊C4—271no—
943C22⋊C4—31no—
944C22⋊C4—31no—
945C22⋊C4—91no—
946C22⋊C4—91no—
947C22⋊C4—91no—
948C22⋊C4—91no—
949C22⋊C4—91no—
950C22⋊C4—91no—
951C22⋊C4—271no—
952C22⋊C4—271no—
953C22⋊C4—271no—
954C22⋊C4—271no—
955C22⋊C4—271no—
956C22⋊C4—271no—
957C42—91no—
958C42—91no—
959C22×C3—21no—
960C22×C3—21no—
961C22×C3—21no—
962C22×C3—41no—
963C22×C3—62no—
964C22×C3—61no—
965C22×C3—61no—
966C22×C3—61no—
967C22×C3—61no—
968C22×C3—61no—
969C22×C3—61no—
970C22×C3—61no—
971C22×C3—61no—
972C22×C3—61no—
973C22×C3—61no—
974C22×C3—61no—
975C22×C3—61no—
976C22×C3—121no—
977C22×C3—121no—
978C22×C3—121no—
979C22×C3—121no—
980C22×C3—121no—
981C22×C3—181no—
982C22×C3—181no—
983C22×C3—181no—
984C22×C3C22×D3211yescharacteristic
985C22×C3C22×D3211yescharacteristic
986C22×C3C22×D3211yescharacteristic
987C2×D3—21no—
988C2×D3—21no—
989C2×D3—21no—
990C2×D3—21no—
991C2×D3—21no—
992C2×D3—21no—
993C2×D3—62no—
994C2×D3—61no—
995C2×D3—61no—
996C2×D3—61no—
997C2×D3—61no—
998C2×D3—61no—
999C2×D3—61no—
1000C2×D3—92no—
1001C2×D3—92no—
1002C2×D3—92no—
1003C2×D3—121no—
1004C2×D3—121no—
1005C2×D3—182no—
1006C2×D3—182no—
1007C2×D3—182no—
1008C2×D3—181no—
1009C2×D3—181no—
1010C2×D3—181no—
1011C2×D3—181no—
1012C2×D3—181no—
1013C2×D3—181no—
1014C2×D3—182no—
1015C2×D3—181no—
1016C2×D3—181no—
1017C2×D3—181no—
1018C2×D3—181no—
1019C2×D3—181no—
1020C2×D3—181no—
1021C2×D3—181no—
1022C2×D3—181no—
1023C2×D3—181no—
1024C2×D3—362no—
1025C2×D3—361no—
1026C2×D3—361no—
1027C2×D3—361no—
1028C2×D3—361no—
1029C2×D3—361no—
1030C2×D3—361no—
1031C2×D3—361no—
1032C2×D3—361no—
1033C2×D3—361no—
1034C2×D3—361no—
1035C2×D3—361no—
1036C2×D3—361no—
1037C2×D3—361no—
1038C2×D3—361no—
1039C2×D3—362no—
1040C2×D3—364no—
1041C2×D3—364no—
1042C2×D3—364no—
1043C2×D3—368no—
1044C2×D3—721no—
1045C2×D3—721no—
1046C2×D3—721no—
1047C2×D3—721no—
1048C3×C4—22no—
1049C3×C4—21no—
1050C3×C4—21no—
1051C3×C4—21no—
1052C3×C4—41no—
1053C3×C4—41no—
1054C3×C4—42no—
1055C3×C4—61no—
1056C3×C4—61no—
1057C3×C4—61no—
1058C3×C4—61no—
1059C3×C4—61no—
1060C3×C4—61no—
1061C3×C4—61no—
1062C3×C4—61no—
1063C3×C4—121no—
1064C3×C4—121no—
1065C3×C4—121no—
1066C3×C4—121no—
1067C3×C4—181no—
1068C3×C4—181no—
1069C3×C4—181no—
1070C3×C4—181no—
1071C3×C4—181no—
1072Dic3—21no—
1073Dic3—21no—
1074Dic3—21no—
1075Dic3—21no—
1076Dic3—62no—
1077Dic3—62no—
1078Dic3—61no—
1079Dic3—61no—
1080Dic3—61no—
1081Dic3—61no—
1082Dic3—61no—
1083Dic3—61no—
1084Dic3—61no—
1085Dic3—61no—
1086Dic3—61no—
1087Dic3—61no—
1088Dic3—121no—
1089Dic3—121no—
1090Dic3—121no—
1091C32—21no—
1092C32—21no—
1093C32—21no—
1094C32—41no—
1095C32#565711yescharacteristic, complemented
1096C32#567811yescharacteristic, complemented
1097C32#570411yescharacteristic, complemented
1098C23—31no—
1099C23—31no—
1100C23—91no—
1101C23—271no—
1102C23—271no—
1103C23—542no—
1104C23—1081no—
1105C23—1081no—
1106Q8—361no—
1107D4—361no—
1108D4—361no—
1109D4—542no—
1110D4—542no—
1111D4—1081no—
1112D4—1081no—
1113D4—1081no—
1114C2×C4—31no—
1115C2×C4—31no—
1116C2×C4—31no—
1117C2×C4—31no—
1118C2×C4—91no—
1119C2×C4—91no—
1120C2×C4—91no—
1121C2×C4—91no—
1122C2×C4—91no—
1123C2×C4—361no—
1124C2×C4—1081no—
1125C2×C4—1081no—
1126C2×C4—1081no—
1127C2×C4D3311yescharacteristic
1128C2×C3—21no—
1129C2×C3—21no—
1130C2×C3—21no—
1131C2×C3—21no—
1132C2×C3—21no—
1133C2×C3—21no—
1134C2×C3—21no—
1135C2×C3—21no—
1136C2×C3—21no—
1137C2×C3—41no—
1138C2×C3—41no—
1139C2×C3—41no—
1140C2×C3—122no—
1141C2×C3—121no—
1142C2×C3—121no—
1143C2×C3—121no—
1144C2×C3—121no—
1145C2×C3—241no—
1146C2×C3—361no—
1147C2×C3#6430611yescharacteristic
1148C2×C3#6430711yescharacteristic
1149C2×C3#6430811yescharacteristic
1150C2×C3#6431211yescharacteristic
1151C2×C3#6431211yescharacteristic
1152C2×C3#6431411yescharacteristic
1153C2×C3#6431411yescharacteristic
1154C2×C3#6431411yescharacteristic
1155C2×C3#6432011yescharacteristic
1156D3—41no—
1157D3—41no—
1158D3—122no—
1159D3—121no—
1160D3—121no—
1161D3—182no—
1162D3—182no—
1163D3—182no—
1164D3—362no—
1165D3—362no—
1166D3—362no—
1167D3—362no—
1168D3—361no—
1169D3—361no—
1170D3—361no—
1171D3—722no—
1172D3—721no—
1173D3—721no—
1174D3—722no—
1175C22—61no—
1176C22—61no—
1177C22—61no—
1178C22—61no—
1179C22—61no—
1180C22—61no—
1181C22—181no—
1182C22—181no—
1183C22—181no—
1184C22—272no—
1185C22—541no—
1186C22—541no—
1187C22—541no—
1188C22—541no—
1189C22—541no—
1190C22—1084no—
1191C22C2×D3311yescharacteristic
1192C4—21no—
1193C4—61no—
1194C4—61no—
1195C4—61no—
1196C4—61no—
1197C4—181no—
1198C4—181no—
1199C4—181no—
1200C4—181no—
1201C4—181no—
1202C3—21no—
1203C3—21no—
1204C3—21no—
1205C3—41no—
1206C3#1059416211yescharacteristic, complemented
1207C3#1059430711yescharacteristic, complemented
1208C3#1059465711yescharacteristic, complemented
1209C2—121no—
1210C2—121no—
1211C2—361no—
1212C2—542no—
1213C2—1081no—
1214C2#1172438411yescharacteristic
1215C2#1172438611yescharacteristic
1216C2#1172441111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11723676C2semidirect
2. #11723542C2semidirect
3. #11723525C2semidirect
4. #11723494C2semidirect
5. C3×#63915C2semidirect
6. C3×#63890C2semidirect
7. C3×#63858C2semidirect
8. #11723003C2semidirect
9. #11722996C2semidirect
10. #11722973C2semidirect
11. #11722963C2semidirect
12. #11722958C2semidirect
13. #11722949C2semidirect
14. #11722932C2semidirect
15. #11722906C2semidirect
24. C2×#6291C22semidirect
27. C2×#6289C22semidirect
28. C2×C3×#627C22semidirect
31. C2×C3×D3×Dic3C22semidirect
33. C3×#3750C22semidirect
34. C3×C4×C3⋊Dic3C22semidirect
36. C32×(C2×D3)⋊C4C22semidirect
37. C32×C4⋊Dic3C22semidirect
38. #88815C22semidirect
39. #88815C22semidirect
44. #88804C22semidirect
45. #88804C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
78. #63915D3semidirect
90. #63890D3semidirect
98. #63858D3semidirect
161. C2×#627C2×D3semidirect
185. C2×D3×Dic3C2×D3semidirect
194. #3750C2×D3semidirect
195. C4×C3⋊Dic3C2×D3semidirect
213. C3×(C2×D3)⋊C4C2×D3semidirect
214. C3×(C2×D3)⋊C4C2×D3semidirect
218. C3×C4⋊Dic3C2×D3semidirect
219. C3×C4⋊Dic3C2×D3semidirect
236. Dic3⋊Dic3C2×D3semidirect
237. Dic3⋊Dic3C2×D3semidirect
260. (C2×D3)⋊Dic3C2×D3semidirect
261. Dic32C2×D3semidirect
581. (C2×D3)⋊C4D32semidirect
586. C4⋊Dic3D32semidirect
748. C33#538semidirect
1095. C32#5657semidirect
1096. C32#5678semidirect
1097. C32#5704semidirect
1206. C3#10594162semidirect
1207. C3#10594307semidirect
1208. C3#10594657semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117236762
#117235422
#117235252
#117234942
C3×#639152
C3×#638902
C3×#638582
#117230032
#117229962
#117229732
#117229632
#117229582
#117229492
#117229322
#117229062
#105946573
#105943073
#105941623